If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x + I) exists in R/I, How do you prove that r^2=8 + I?
If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x + I) exists in R/I, How do you prove that r^2=8 + I?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x + I) exists in R/I, How do you prove that r^2=8 + I?
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